We report the high-field induced magnetic phases and phase diagram of a high quality urxrs~single crystal prepared using a modified Czochralski method. Our study, that combines high-field magnetization and electrical resistivity measurements, shows for fields applied along the $c$-axis direction three field-induced magnetic phase transitions at $mu_{0} H_{c1}$ = 21.60 T, $mu_{0} H_{c2}$ = 37.90 T and $mu_{0} H_{c3}$ = 38.25 T, respectively. In agreement with a microscopic up-up-down arrangement of the U magnetic moments the phase above $H_{c1}$ has a magnetization of about one third of the saturated value. In contrast the phase between $H_{c2}$ and $H_{c3}$ has a magnetization that is a factor of two lower than above the $H_{c3}$, where a polarized Fermi-liquid state with a saturated moment $M_{s}$ $approx$ 2.1 $mu_{B}$/U is realized. Most of the respective transitions are reflected in the electrical resistivity as sudden drastic changes. Most notably, the phase between $H_{c1}$ and $H_{c2}$ exhibits substantially larger values. As the temperature increases, transitions smear out and disappear above $approx$ 15 K. However, a substantial magnetoresistance is observed even at temperatures as high as 80 K. Due to a strong uniaxial magnetocrystalline anisotropy a very small field effect is observed for fields apllied perpendicular to the $c$-axis direction.
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